• Corpus ID: 248834609

On partially observed jump diffusions I. The filtering equations

  title={On partially observed jump diffusions I. The filtering equations},
  author={Fabian Germ and Istvan Gyongy},
. This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the equation only satisfy appropriate growth conditions. Some results in filtering theory of diffusion processes are extended to jump diffusions and equations for the time evolution of the conditional distribution and the unnormalised conditional distribution of the unobserved… 
On partially observed jump diffusions II. The filtering density
Abstract. A partially observed jump diffusion Z “ pXt, YtqtPr0,T s given by a stochastic differential equation driven by Wiener processes and Poisson martingale measures is considered when the


Nonlinear Filtering for Jump Diffusion Observations
We deal with the filtering problem of a general jump diffusion process, X, when the observation process, Y, is a correlated jump diffusion process having common jump times with X. In this setting, at
Nonlinear filtering of Itô-Lévy stochastic differential equations with continuous observations
We study the n-dimensional nonlinear filtering problem for jumpdiffusion processes. The optimal filter is derived for the case when the observations are continuous. A proof of uniqueness is presented
Nonlinear filtering with correlated L\'evy noise characterized by copulas
The objective in stochastic filtering is to reconstruct information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy
On the Innovations Conjecture of Nonlinear Filtering with Dependent Data
We establish the innovations conjecture for a nonlinear filtering problem in which the signal to be estimated is conditioned by the observations. The approach uses only elementary stochastic
Nonlinear filtering for jump-diffusions
Nonlinear filtering of stochastic differential equations driven by correlated L\'evy noises.
The work concerns nonlinear filtering problems of stochastic differential equations with correlated L\'evy noises. First, we establish the Kushner-Stratonovich and Zakai equations through martingale
The Zakai Equation of Nonlinear Filtering for Jump-Diffusion Observations: Existence and Uniqueness
In this paper we study a nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any
A Direct Approach to Deriving Filtering Equations for Diffusion Processes
Abstract. Filtering equations are derived for conditional probability density functions in case of partially observable diffusion processes by using results and methods from the Lp -theory of SPDEs.
The filtering equations revisited
The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of–probability-measure method introduced by
Lévy Processes and Stochastic Calculus
Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random