Related papers: A Causal Construction of Diffusion Processes
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Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Extending It\^o's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It\^o, applies to one dimensional semimartingales and convex functions.…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
In this paper we re-examine the traditional problem of connecting the internal fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With…
A causal scattering matrix is constructed by means of the mixed chronological and normal product of the free quantum fields of different variables. This scattering matrix does not contain the diverging integrals.
When the causal relationship between X and Y is specified by a structural equation, the causal effect of X on Y is the expected rate of change of Y with respect to changes in X, when all other variables are kept fixed. This causal effect is…
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In cond-mat/0103603 Diffusion algebras have been introduced in the context of one-dimensional stochastic processes with exclusion in statistical mechanics. While this reference is focused on the needs of the physicist reader and thus states…
We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out…
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…
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We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Ito equations are derived for simple stochastic cellular automaton with parameters and compared with results obtained from the histogram method. Good agreement for various parameters supports wide applicability of the Ito equation as a…
We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…
We study causal effect estimation in a setting where the data are not i.i.d. (independent and identically distributed). We focus on exchangeable data satisfying an assumption of independent causal mechanisms. Traditional causal effect…