Related papers: A Closed-Form Approximation of Likelihood Function…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed,…
Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
We propose a homotopy continuation method called FLUX for approximating complicated probability density functions. It is based on progressive processing for smoothly morphing a given density into the desired one. Distributed ordinary…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
We propose Diffusion Model Variational Inference (DMVI), a novel method for automated approximate inference in probabilistic programming languages (PPLs). DMVI utilizes diffusion models as variational approximations to the true posterior…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities…
We re-visit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those…
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…