Subordinator
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ASYMPTOTIC BEHAVIORS OF FUNDAMENTAL SOLUTION AND ITS DERIVATIVES TO FRACTIONAL DIFFUSION-WAVE EQUATIONS Open
Let p (t, x) be the fundamental solution to the problem partial derivative(alpha)(t) u = -(-Delta)(beta)u, alpha is an element of (0, 2), beta is an element of (0, infinity). If alpha, beta is an element of (0, 1), then the kernel p (t, x)…
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Some Properties of the Kilbas-Saigo Function Open
We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at −∞, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le…
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Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators Open
In recent years subordinated processes have been widely considered in the literature. These processes not only have wide applications but also have interesting theoretical properties. In this paper we consider fractional Brownian motion (F…
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Lévy-walk-like Langevin dynamics Open
Continuous-time random walks and Langevin equations are two classes of stochastic models used to describe the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more o…
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A generalization of the space-fractional Poisson process and its connection to some Lévy processes Open
The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We intro…
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Heterosemy of case markers and clause-linkers in Andaandi (Nile Nubian) Open
Case markers are usually associated with nouns or noun phrases but, as shown in Aikhenvald’s (2008) cross-linguistic study on “versatile cases”, case markers are also used as clause-linkers in a wide range of genetically diverse languages.…
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Quantum walks with sequential aperiodic jumps Open
We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse, and Rudin-Shapiro. We use a generalized Hadamard coin, C…
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Potential theory of subordinate killed Brownian motion Open
Let $W^D$ be a killed Brownian motion in a domain $D\subset \mathbb {R}^d$ and $S$ an independent subordinator with Laplace exponent $\phi$. The process $Y^D$ defined by $Y^D_t=W^D_{S_t}$ is called a subordinate killed Brownian motion. It …
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Tempered fractional Langevin–Brownian motion with inverse<i>β</i>-stable subordinator Open
Time-changed stochastic processes have attracted much attention and wide interest due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process, tem…
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Subgeometric rates of convergence for Markov processes under subordination Open
We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent), we characterize the convergence rate of the subordinat…
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Continuous-state branching processes with competition: duality and\n reflection at Infinity Open
The boundary behavior of continuous-state branching processes with quadratic\ncompetition is studied in whole generality. We first observe that despite\ncompetition, explosion can occur for certain branching mechanisms. We obtain a\nnecess…
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Estimates of Dirichlet heat kernels for subordinate Brownian motions Open
In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large …
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Limits of multiplicative inhomogeneous random graphs and Levy trees Open
We consider a natural model of inhomogeneous random graphs that extends the classical Erdos-Renyi graphs and shares a close connection with the multiplicative coalescence, as pointed out by Aldous . In this model, the vertices are assigned…
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Space‐time fractional Dirichlet problems Open
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time‐changed by an inverse stable subordinator whose index equals the order of…
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Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics Open
It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wideinterest in statistical physics as they are …
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Modeling temperature and pricing weather derivatives based on subordinate Ornstein-Uhlenbeck processes Open
In this paper we employ a time-changed Ornstein-Uhlenbeck (OU) process for modeling temperature and pricing weather derivatives, where the time change process is a Lévy subordinator time changed by a deterministic clock with seasonal activ…
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Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting Open
We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358-1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345-358, 2008) hold under more simplified conditions. Moreover, we…
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Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex Open
The Poisson-Kingman distributions, $\mathrm{PK}(ρ)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $ρ$ or by taking the ranked jumps up till a specified time of a subordinator with Lévy d…
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Formal and quantitative approaches to the study of syntactic change: three case studies from the history of English Open
Linguistic changes involving competition between two alternative forms are investigated with three case studies on syntactic changes from the history of English. First, evidence is produced for the hypothesis that a linguistic innovation s…
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Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing Open
In this paper we present a novel model to analyze the behavior of random asset price process under the assumption that the stock price pro-cess is governed by time-changed generalized mixed fractional Brownian motion with an inverse gamma …
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Pricing credit derivatives under a correlated regime-switching hazard processes model Open
In this paper, we study the valuation of a single-name credit default swap and a $k$th-to-default basket swap under a correlated regime-switching hazard processes model. We assume that the defaults of all the names are driven by a Markov c…
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Diffusions on a space of interval partitions: construction from marked Lévy processes Open
Consider a spectrally positive Stable($1+α$) process whose jumps we interpret as lifetimes of individuals. We mark the jumps by continuous excursions assigning "sizes" varying during the lifetime. As for Crump-Mode-Jagers processes (with "…
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Multivariate tempered stable additive subordination for financial models Open
We study a class of multivariate tempered stable distributions and introduce the associated class of tempered stable Sato subordinators. These Sato subordinators are used to build additive inhomogeneous processes by subordination of a mult…
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On the boundary theory of subordinate killed Lévy processes Open
Let $Z$ be a subordinate Brownian motion in ${\mathbb R}^d$, $d\ge 2$, via a subordinator with Laplace exponent $ϕ$. We kill the process $Z$ upon exiting a bounded open set $D\subset {\mathbb R}^d$ to obtain the killed process $Z^D$, and t…
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A recursive pricing method for autocallables under multivariate subordination Open
In this paper we develop a new class of models for pricing autocallables based on multivariate subordinate Orstein Uhlenbeck (OU) processes. Starting from d independent OU processes and an independent d-dimensional Lévy subordinator, we co…
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Stochastic models with mixtures of tempered stable subordinators Open
In this article, we introduce mixtures of tempered stable subordinators (TSS). These mixtures define
\na class of subordinators which generalize tempered stable subordinators. The main properties like probability
\ndensity function (pdf), …
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Precise asymptotics for the density and the upper tail of exponential functionals of subordinators Open
We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour o…
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Scaling limit of sub-ballistic 1D random walk among biased conductances: a story of wells and walls Open
We consider a one-dimensional random walk among biased i.i.d. conductances, in the case where the random walk is transient but sub-ballistic: this occurs when the conductances have a heavy-tail at $+\\infty $ or at $0$. We prove that the s…
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Limit theorems for prices of options written on semi-Markov processes Open
We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in wh…
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On the inverse gamma subordinator Open
In this paper we deal with some open problems concerned with Gamma subordinators. In particular, we first provide a representation for the moments of the inverse gamma subordinator. Then, we focus on λ-potentials and we study the governing…