Related papers: Invariant cones for jump-diffusions in infinite di…

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…

Based on a recent result on characterising the path-independence of the Girsanov transformation for non-Lipschnitz stochastic differential equations (SDEs) with jumps on $R^d$, in this paper, we extend our consideration of characterising…

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties…

Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such applications include non-globally monotone nonlinearities.…

The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is…

In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…

This paper investigates parameter estimation for open quantum systems under continuous observation, whose conditional dynamics are governed by jump-diffusion stochastic master equations (SMEs) associated with quantum nondemolition (QND)…

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every…

We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic…

In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison…

We consider a solution to a generic Markovian jump diffusion and show that for positive times the law of the solution process has a smooth density with respect to Lebesgue measure under a uniform version of Hoermander's conditions. Unlike…

Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…

In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the…

In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-called "viability property". As an application, we study the…

This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant…