scholarly journals A jump persistent turning walker to model zebrafish locomotion

2015 ◽  
Vol 12 (102) ◽  
pp. 20140884 ◽  
Author(s):  
Violet Mwaffo ◽  
Ross P. Anderson ◽  
Sachit Butail ◽  
Maurizio Porfiri
Keyword(s):  
Diffusion Model ◽  
Empirical Distribution ◽  
Critical Role ◽  
Jump Process ◽  
Trajectory Data ◽  
Heavy Tailed Distributions ◽  
Theoretical Predictions ◽  
Jump Diffusion Model ◽  
Heavy Tailed ◽  
Turn Rate

Zebrafish are gaining momentum as a laboratory animal species for the investigation of several functional and dysfunctional biological processes. Mathematical models of zebrafish behaviour are expected to considerably aid in the design of hypothesis-driven studies by enabling preliminary in silico tests that can be used to infer possible experimental outcomes without the use of zebrafish. This study is motivated by observations of sudden, drastic changes in zebrafish locomotion in the form of large deviations in turn rate. We demonstrate that such deviations can be captured through a stochastic mean reverting jump diffusion model, a process that is commonly used in financial engineering to describe large changes in the price of an asset. The jump process-based model is validated on trajectory data of adult subjects swimming in a shallow circular tank obtained from an overhead camera. Through statistical comparison of the empirical distribution of the turn rate against theoretical predictions, we demonstrate the feasibility of describing zebrafish as a jump persistent turning walker. The critical role of the jump term is assessed through comparison with a simplified mean reversion diffusion model, which does not allow for describing the heavy-tailed distributions observed in the fish turn rate.

scholarly journals Assessing The Relative Performance Of Heavy-Tailed Distributions: Empirical Evidence From The Johannesburg Stock Exchange

2014 ◽  
Vol 30 (4) ◽  
pp. 1263 ◽  
Author(s):  
Chun-Sung Huang ◽  
Chun-Kai Huang ◽  
Knowledge Chinhamu
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Stock Exchange ◽  
Vital Role ◽  
Financial Data ◽  
Johannesburg Stock Exchange ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

<p>It has been well documented that the empirical distribution of daily logarithmic returns from financial market variables is characterized by excess kurtosis and skewness. In order to capture such properties in financial data, heavy-tailed and asymmetric distributions are required to overcome shortfalls of the widely exhausted classical normality assumption. In the context of financial forecasting and risk management, the accuracy in modeling the underlying returns distribution plays a vital role. For example, risk management tools such as value-at-risk (VaR) are highly dependent on the underlying distributional assumption, with particular focus being placed at the extreme tails. Hence, identifying a distribution that best captures all aspects of the given financial data may provide vast advantages to both investors and risk managers. In this paper, we investigate major financial indices on the Johannesburg Stock Exchange (JSE) and fit their associated returns to classes of heavy tailed distributions. The relative adequacy and goodness-of-fit of these distributions are then assessed through the robustness of their respective VaR estimates. Our results indicate that the best model selection is not only variant across the indices, but also across different VaR levels and the dissimilar tails of return series.</p>

scholarly journals Heavy-tailed distributions in a stochastic gene autoregulation model

2021 ◽  
Author(s):  
Pavol Bokes
Keyword(s):  
Large Deviations ◽  
Stationary Distribution ◽  
Burst Size ◽  
Cumulative Effect ◽  
Jump Process ◽  
Gene Products ◽  
Tail Region ◽  
Expression Variability ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

Synthesis of gene products in bursts of multiple molecular copies is an important source of gene expression variability. This paper studies large deviations in a Markovian drift--jump process that combines exponentially distributed bursts with deterministic degradation. Large deviations occur as a cumulative effect of many bursts (as in diffusion) or, if the model includes negative feedback in burst size, in a single big jump. The latter possibility requires a modification in the WKB solution in the tail region. The main result of the paper is the construction, via a modified WKB scheme, of matched asymptotic approximations to the stationary distribution of the drift--jump process. The stationary distribution possesses a heavier tail than predicted by a routine application of the scheme.

The Pricing of Vulnerable Options Under Jump-Diffusion Model

2013 ◽  
Vol 15 (3) ◽  
pp. 204
Author(s):  
Chixiang CHEN ◽  
Biyi SHEN ◽  
Guangyu YANG
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Jump Diffusion Model ◽  
Vulnerable Options

MCMC estimation of a multi-factor jump diffusion model for power prices

2008 ◽  
Vol 1 (4) ◽  
pp. 65-90 ◽  
Author(s):  
Rikard Green ◽  
Marcus Nossman
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Mcmc Estimation ◽  
Jump Diffusion Model
Sign in / Sign up

Export Citation Format

Share Document