Related papers: Support theorems for degenerate stochastic differe…
In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…
We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…
We provide a support theorem for the law of the solution to an SDE with jump noise. This theorem applies to general SDEs with jumps and is illustrated by examples of SDEs with quite degenerate jump noises where the theorem leads to an…
In this paper, we derive a characterization theorem for the path-independent property of the density of the Girsanov transformation for {\it degenerated} stochastic differential equations (SDEs), extending the characterization theorem of…
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…
This paper establishes a converse comparison theorem for real-valued decoupled forward backward stochastic differential equations with jumps.
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…
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
In this note, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional stochastic differential equations (SDEs) with jumps and for matrix-valued SDEs with jumps.
We consider one-dimensional stochastic differential equations with jumps in the general case. We introduce new technics based on local time and we prove new results on pathwise uniqueness and comparison theorems. Our approach are very easy…
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…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
We obtain sufficient condition for SDEs to evolve in the positive orthant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs…
In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
In this paper we prove the existence and uniqueness theorem, comparison theorem of a class of anticipated mean-field backward stochastic differential equations with jumps.
In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of…