Related papers: Integration by parts formula for killed processes:…
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…
In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an integration by parts formula for the first exit time of…
We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as…
We introduce a probabilistic representation of the derivative of the semigroup associated to a multidimensional killed diffusion process defined on the half-space. The semigroup derivative is expressed as a functional of a process that is…
Affine processes play an important role in mathematical finance and other applied areas due to their tractable structure. In the present article, we derive probabilistic representations and integration by parts (IBP) formulas for…
We consider random variables of the form $F=f(V_1,...,V_n)$, where $f$ is a smooth function and $V_i,i\in\mathbb{N}$, are random variables with absolutely continuous law $p_i(y) dy$. We assume that $p_i$, $i=1,...,n$, are piecewise…
An integration by parts formula is the foundation for stochastic analysis on path spaces over a (finite dimensional) Riemannian manifold or over $R^n$, from which we may deduce the operator $d$ is closable and define the Laplacian operator…
We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps, including equations with discontinuous coefficients…
Probabilistic inference provides a language for describing how organisms may learn from and adapt to their environment. The computations needed to implement probabilistic inference often require specific representations, akin to having the…
Integration by parts formulae are given for a class of measures on the space of paths of a smooth manifold $M$ determined by the laws of degenerate diffusions. The mother of such formulae, on the path space of diffeomorphism group of $M$ is…
Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with…
We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are…
Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…
In this paper we develop a stochastic analysis for marked binomial processes, that can be viewed as the discrete analogues of marked Poisson processes. The starting point is the statement of a chaotic expansion for square-integrable (marked…
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…